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Physics 4A
Measurement Worksheet
Introduction:
This preliminary exercise (Individualized, No Lab Partners) is designed to provide
a "hands-on" review of measurement, which will include: some familiar or unfamiliar instruments, some
SI units, the measuring process, significant figures, derived quantites, and graphing. Before beginning
this important exercise, please read the "Significant Figures", "Graphical Analysis Handout", “The Lab
Manual Handout”, and “The Vernier & Micrometer” handouts.
Part 1: Measurement & SI Units
Directions: Measure the following quantities and report them in the indicated units. Be sure to
report the correct number of significant figures.
A. What is d in centimeters?
0
1
cm
d=
____________ cm
3
2
d
B. During the semester, you will be using verniers calipers to measuring objects in
centimeters (cm). Record the caliper reading shown below (Each small division on the
scale below is one mm.) When you use the vernier calipers in the lab, make sure you
read the correct scale since some of the calipers have both inch and centimeter scales.
1.
__________
0
1
2
4
3
0
cm
10
2.
__________
0
1
2
0
10
1
2
3
4
3
4
3.
cm
__________
0
0
1
10
cm
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C. Obtain three wires. Use a Micrometer to measure their
Diameter (indicate color of wire):
a. __________ mm
b. __________ mm
c. __________ mm
D. Obtain a sheet of white copy paper and measure its
a. length :
__________ cm
b. width:
c. thickness: __________ cm
__________ cm
d. mass: __________ g
E. Measure Room
Temperature: __________ deg C
F. Measure  by rolling a cylinder out on a piece of paper. Use a Vernier caliper to measure d.
C = __________
d = __________
 = __________
% Error = __________
F. Determine the density of H2O.
Mass of Graduate: __________
Mass of H2O: __________
Mass of Graduate + H2O: __________
Volume of H2O: __________ Density: __________
Part 2: Significant Figures & Derived Quantities
Directions: Carry out the indicated operations below and report the answer to the correct number of
significant figures in the space provided.
1. 145.6  6.2 
__________
2.
53.87
 __________
0.0835
3. 126.34 12.785  __________
4.
123.15m2  __________
377.55m  5.0m
 __________
32.1s
6.
0.975  0.04
 __________
2.061
5.
7.
0.011 has
__________ sig. figs
8. 64,340 has __________
9. Write 57,440 to 4 sig. figs using scientific notation: __________
2
sig. figs
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10. Calculate the average of the following measurements (don’t forget to apply the rules for
sig figs): 2.06cm, 2.18cm, 2.05cm, 2.10cm, 2.11cm, 2.09cm. __________
Express your answers to the following in scientific notation:
11. Add 5.80 x 103 and 6.75 x 102 =
__________
12. Multiply 6.687 x 10-3 and 479 x 10-4 = _________
13. Divide 1398 x 10-4 by 8.8469 x 10-3 = __________
Part 3: Graphing
A. Obtain the beaker of pennies, place one on the centigram balance, and measure its mass in grams.
Record this mass in a data table made on a separate piece of paper. Now add a penny and measure
the mass of both pennies and record in your table. Continue adding pennies, and measuring and
recording the total mass for a total of at least fifteen pennies. Now plot a graph of mass vs. number
of pennies and evaluate the slope (show your calculation below your data table).
Number
Mass of
of Pennies Pennies (g)
Penny
Penny
Mass (g)
Does your slope have units? Explain. ____________________________________
What does the slope mean? __________________________________
Be sure to attach your data table and graph to this worksheet.
What is the slope of your graph to the correct number of decimal places?____________
B. Weigh each of the pennies individually and list their masses in a table.
Calculate their average mass.
_____________________
How does this compare to the slope of the graph? Why?
________________________________________________________________________
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s
Calculate the standard deviation from the mean.
(always keep one sig. fig.)
Calculate the precision the mean  m 
_____________________
(always keep one sig. fig.)
s
N

 xi  x 
2
N 1
_____________________
.
What is the precision of the balance?
_____________________
(always keep one sig. fig.)
What does the standard deviation of the mean tell you?
How does the precision of the mean compare to the precision of the balance? Should they be the
same in this experiment? Why or Why not?
Part 4 Propagation of Errors
Measure the diameter of the given sphere with the Vernier caliper.
What is precision of your Vernier caliper?
D=__________cm
D=__________cm
Using your knowledge of differential calculus (refer to your calculus textbook), estimate the error in
the volume of the sphere. Show your work below.
V=__________cm3
Use a Vernier caliper to measure the block’s length, L, width, W, and height, H, five times. Make
sure you use different locations on the block when you repeat each measurement. Then calculate the
average length, width, and height along with their uncertainties. Report values using the format
LL, WW, and HH. Finally calculate the average volume of the block along with its
uncertainty (using the proper method to propagate the errors).
Trial Number
1
2
3
4
5
Average Length
=
Average Width
=
Average Height
=
(Lavg ) (Wavg ) (Havg )=
Length(cm)
Width(cm)
Height (cm)
___________cm
___________cm
___________cm
___________cm3 = ______________m3
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